The topological trivial band of a lattice can be driven into a topological phase by disorder in the system. This so-called topological Anderson phase has been predicted and observed for uncorrelated static disorder, while in the presence of correlated disorder, conflicting results are found. Here we consider a Su–Schrieffer–Heeger waveguide lattice in the trivial topological phase and show that quasi-periodic disorder in the coupling constants can drive the lattice into a topological nontrivial phase. A method to detect the emergence of the topological Anderson phase, based on light dynamics at the edge of a quasi-periodic waveguide lattice, is suggested.